الرابع: جد ناتج احد التكاملين التالي ين 1- Smte) xy e*y° dxdy 2- r? N4-y² ry8-x²-y" zdzdxdy x²+y2 2- Só S

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: Integrate S(csc 3x + cot 3x)²dx A. cot 3x –csc 3x –x+ C -cot 3x -csc 3x – x+C -를cot 3x- sc 3x + x +C…

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Q: What is the coefficient of x2y" in (5x- y)°?

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Q: dr –DA V7 - 5r)

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: oB coser sec 2o -

A: To find the value of 2cosec20°sec20°

Q: S Vi+ V2+3xdx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Differentiate y = xV A. 2Vx (2+In x) В. (2+In x) VX C. 2vx 2V (2 – In x) | D. 2V (2 + In x)

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Q: +タ x2 – 1

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Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: For what value of x, 3x 2х 2:

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Q: Consider the two following graphs and answer the following questions. a) Are G and H isomorphic?…

A: The graphs given are as follows:

Q: What is fxe- dx ? -x Oxe xee+C Ox²e-2x 2 + C X -xe-* — e * +C x² e-x 2 + C

A: Consider,

Q: хt — х +6 dx х3 + Зх

A: We shall use polynomial long division method to simplify our integrand.

Q: A) в) (2х)5 . (Зу)5 c) (ба)6 (20)6 y°

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: 2 x²+yi -I -VI-2²

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Q: If 2x = xy + y2, then A. C. -2 + y x + 2y (2-y) x + 2y dx 11 B. D. -(2 + y) x + 2y -(-2+ y) x + 2xy

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Q: Exc. Eind. Lim (x-1) y3

A: Solution:

Q: The equation below is said to be A. Linear in x O B. Linear in y C. Linear in both x and y O D.…

A: We will find out the required value.

Q: If A = x²zi + xyj + y²zk and B = yz²i+xzj + x²zk determine the expression grad(A.B) at the point…

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Q: Find xy² Una -dA, R= [0,4] × [-2, 2] x² + 1

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Q: Show that the homogenous equation (Ax + By) ⅆx + (Cx + Dy) ⅆy = 0 Is exact if and only if B = C.…

A: Please refer the attached image for complete solution.

Q: dx xV4x-1

A: To find: The integral of ∫dxx4x-1. Formula used: Integration formula: ∫dxx2+1=tan-1x+C

Q: b. 3+V5-x 3I

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Q: b) 2(x4+1)5 dx

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Q: 2a - 5y dA, R =(-5,4] x [0, 3] R.

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Q: -5x y"+ 3y- 10y = - 14 xe

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.